Hierarchical perception of melody

Proceedings of the 7th Triennial Conference of European Society for the Cognitive Sciences of Music (ESCOM 2009) Jyväskylä, Finland Jukka Louhivuori, ...
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Proceedings of the 7th Triennial Conference of European Society for the Cognitive Sciences of Music (ESCOM 2009) Jyväskylä, Finland Jukka Louhivuori, Tuomas Eerola, Suvi Saarikallio, Tommi Himberg, Päivi-Sisko Eerola (Editors)

Hierarchical perception of melody Jens Hjortkjær*1 *

Department of Arts and Cultural Studies, University of Copenhagen, Denmark 1

[email protected]

instance of the melody when performed. Both GTTM and Schenkerian theory claim that structural levels are themselves music (in schenkerian theory reduced levels must adhere to voice leading principles in the same way that actual melodies do). At deeper reductional levels the reduction is descriptive of a range of tonal melodies (the deepest levels of reduction the Schenkerian Urlinie - is precisely a description of the abstract structure that define the work as tonal). It will therefore become increasingly difficult to match deeper reductions with a specific melody.

ABSTRACT Two experiments were designed to investigate the hierarchical perception of melodies. The hierarchical structure of tonal melodies is formally described in Lerdahl and Jackendoff's Generative Theory of Tonal Music (GTTM). The experiments were designed to assess different aspects of GTTM time span reduction quantitatively. Subjects were presented with pairs of melodies in a same-different task. A short novel and a longer original tonal melody could differ within the harmonic context at single tones on one of four time span reduction levels. It was found that detection rate of the melodic deviances correlated strongly with time span level. The same method was employed on an atonal and a poorly composed tonal melody. Detection rates were lower for the atonal but not for the ill-formed melody, and responses still varied significantly with position of the deviant tone. Generally, the correlation of responses with reductional level was found to be much stronger than with alternative musical parameters that could be thought to influence detection rate, such as metrical position. The obtained quantitative measures of hierarchical levels suggest that these are subject to variations not normally envisaged by music analysis. It is suggested that hierarchical levels may be graded in nature, with the perceived hierarchical depth depending on the nature of the melodic sequence.

I.

To overcome this problem a different experimental approach is suggested by the present studies. Instead of presenting musical reductions, melodies were manipulated at individual notes in a same-different task. Analytical reductions of the presented melodies were done and within-harmony deviations were inserted at different time span reduction levels. It was hypothesized that deviations in the melody would be easier to recognize if they belong to deeper time span levels. If the memory representation of a tonal melody constitutes a hierarchical reduction then changes to the reduced levels would change the mental representation of it at a more fundamental level. For instance, tones at or near the beginning or end of a melody usually play an important structural role (like the beginning or end of a narrative), and a change of the melody at such positions would be perceived more readily than changes at other positions. We also speculated that an effect of different recognition rates at different time span levels would increase with longer sequences. Short sequences can be held within short-term memory that is known to represent material in a more direct manner than long-term memory. In a same-different task subjects may try to focus on individual pitches rather than the melodic whole, which will become increasingly difficult for longer melodies.

INTRODUCTION

The ability to perceive musical melodies as meaningful sequences is thought to depend on the formation of a mental hierarchy of events. This is not only the case with music understanding the narrative of a novel or a film depends on the mental ability to distinguish the importance of perceived events in relation to the plot. Structural hierarchies of melodies have been described formally within music theory. The music theory of H. Schenker and the Generative Theory of Tonal Music (GTTM) by F. Lerdahl and R. Jackendoff (1983) are prominent approaches. 'Time span reduction' is the analytical procedure in GTTM by which the structural weight of tones in a melody is assigned. Tones in the musical surface that are considered ornamental are reduced out to arrive at a more fundamental structural level of the melody. This analytical process is iterated to elucidate still deeper structural levels.

The same-different task has been used a variety of studies on music perception. In classic studies Deutsch et al. demonstrated that judgment about the identity of tones in a sequence is heavily affected by the harmonic or melodic nature of other interpolating tones in the sequence (Deutsch & Roll, 1974; Deutsch, 1982). If a tone is perceived as part of a larger gestalt (such as a melodic phrase) then changing the tone may be perceived as a change in the global pitch pattern. This is true of simple pitch patterns that are not part of a tonal melody - deviation to a pattern of pitches ascending stepwise on a diatonic scale is easily perceived. Changes to tones within a melody may also be perceived as a function of such low level auditory processing. However, within the context of a melodic gestalt some elements are more essential in defining the mental representation. An analogy may be drawn to visual perception: in perceiving another person, movements in many parts of the body are processed but even small movements of the face (defining a facial expression) are easily perceived

There has been some experimental support for the cognitive reality of hierarchical perception in tonal music (Deliège, 1987; Castellano et al. 1984; Bharucha, 1987; Large et al., 1995, Bharucha & Krumhansl, 1983; Palmer & Krumhansl 1987). Serafine et al. (1989) presented melodies and performances of structural reductions and asked subjects to match a melody with its reduction. They found that listeners were 'moderately able' to identify the correct reduction. Dibben (1994) used a similar method with similar results. The relatively low recognition rate could be a consequence of methodology. Structural reductions may describe cognitive processes without being perceivable as an

URN:NBN:fi:jyu-2009411258

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Proceedings of the 7th Triennial Conference of European Society for the Cognitive Sciences of Music (ESCOM 2009) Jyväskylä, Finland Jukka Louhivuori, Tuomas Eerola, Suvi Saarikallio, Tommi Himberg, Päivi-Sisko Eerola (Editors)

since they are often essential in defining the visual gestalt of the person (rather than e.g. movements of the shoulders at a similar physical magnitude). In detecting differences in a melody it may be expected that low and high level cognitive processes interact. However, if structural high-level features are strong enough they should outweigh the influence of low-level features in the experimental procedure.

B. Subjects 26 subjects participated in experiment 1 and 11 subjects participated in experiment 2. All participants had either some or much practical musical training. In the experiments, no significant differences in the detection rates were found between subjects as a function of level of training. Consequently, subjects are not differentiated according to levels of musical training in the analysis.

II. METHOD

C. Procedure In both experiments subjects were presented with either unchanged pairs or the original and deviation melody on consecutive trials. For all melodies each deviation were presented 4 times in total. After each pair, subjects had to judge whether the melodies were identical or different by pressing one of two buttons. Half of the presentations were identical pairs in experiment 1, and only 4 presentations were identical in experiment 2. In experiment 1, subjects were presented with the two melodies in separate blocks, whereas the presentations in experiment 2 alternated between the two melodies within the block.

A. Stimuli The two experiments used similar setups and differed primarily in the presented melodies. Four melodies were presented in total, two in each experiment (figure 1). In the first experiment two novel melodies were created (melody 1 and 2). Melody 1 was tonal and melody 2 was atonal. Both melodies were 8 seconds long and had identical rhythms. In the second experiment a precomposed 'real' tonal melody (melody 3) was used (an extract from Isaac Albéniz' España). Before the beginning of the experiment subjects had to indicate whether they knew the melody in advance. Only subjects indicating that they did not know the pre-composed melody in advance were used for analysis.

Melody 1 (tonal, novel, short)

A second ill-formed 'tonal' melody (melody 4) was constructed for experiment 2 by permutation of the order of tones from melody 3. The permutation was created by a random reordering of tones that resulted in correlations with the key profiles given by Krumhansl and Kessler (Krumhansl & Kessler, 1982; Krumhansl, 1990) nearly identical to that of melody 3. Consequently, melody 4 had an identical estimate of tonality by this correlational measure, but lacked the sense of meaningful construction of the precomposed melody 3. A tonal centre could clearly be perceived, but the melody lacked a sense of musical coherence. Melody 3 and 4 used in experiment 2 were both 18 seconds long and were also rhythmically identical.

Melody 2 (atonal, novel, short)

Melody 3 (tonal, precomposed, long)

Each melody could differ in one of four places. In melodies 1 and 3 (tonal) these positions corresponded to four different time span levels of the reductional analysis (figure 1). Time span reduction of the atonal and ill-formed melody (2 and 4) was not attempted, and these melodies deviated in similar positions as those in melodies 1 and 3 respectively. The positions of deviations in the tonal melodies were chosen so as to reduce the influence of surface salience due to low level auditory processing (repeated notes, parallelism etc.). In experiment 1 only one deviation was defined at each position, whereas the melodies in experiment 2 could deviate to two alternative tones for each position. This was done to ensure that heard deviations were perceived as a function of position in the melodic hierarchy, rather than as a change in melodic contour. The melodies in experiment 1 were all presented in the same key, whereas each consecutive presentation was transposed to a new key in experiment 2. The stimuli were generated using frequency modulated tones and presented to subjects in headphones in an isolated room.

URN:NBN:fi:jyu-2009411258

Melody 4 (tonal, ill-formed, long)

Figure 1. Presented melodies. Melodies 1 and 2 were presented in experiment 1; melodies 3 and 4 were presented in experiment 2. Numbers above deviating tones correspond to analysed time span level (for melodies 1 and 3) of the melodic position (level 1 is the musical surface, and level 4 is the deepest level of reduction)

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Proceedings of the 7th Triennial Conference of European Society for the Cognitive Sciences of Music (ESCOM 2009) Jyväskylä, Finland Jukka Louhivuori, Tuomas Eerola, Suvi Saarikallio, Tommi Himberg, Päivi-Sisko Eerola (Editors)

III. RESULTS

The mean correct responses for the tonal melody also indicate that deviant tones at deeper time span levels are better detected. The overall linear correlation between time span levels and correct responses was found to be strong (r = .88). Tones at levels 3 and 4 are roughly at the same level of detection though. This is most likely explained by the fact that many subjects were able to detect every deviation at these levels, and would imply the need to increase the difficulty of the task. In Experiment 2 longer melodies was used to achieve this.

A. Experiment 1 As indicated in figures 2 and 3 below, responses on different-trials are highly dependent on the deviant tone in both melodies. Two-way analysis of variance (deviations, subjects) showed that the difference in response to individual deviations were highly significant between subjects in both melodies (melody 1 (tonal): F(4,26)=38.42, p

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